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Simplifying t2 + -1t = 0.20 Reorder the terms: -1t + t2 = 0.20 Solving -1t + t2 = 0.20 Solving for variable 't'. Reorder the terms: -0.20 + -1t + t2 = 0.20 + -0.20 Combine like terms: 0.20 + -0.20 = 0.00 -0.20 + -1t + t2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.20' to each side of the equation. -0.20 + -1t + 0.20 + t2 = 0.00 + 0.20 Reorder the terms: -0.20 + 0.20 + -1t + t2 = 0.00 + 0.20 Combine like terms: -0.20 + 0.20 = 0.00 0.00 + -1t + t2 = 0.00 + 0.20 -1t + t2 = 0.00 + 0.20 Combine like terms: 0.00 + 0.20 = 0.2 -1t + t2 = 0.2 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 0.2 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 0.2 + 0.25 Combine like terms: 0.2 + 0.25 = 0.45 0.25 + -1t + t2 = 0.45 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 0.45 Calculate the square root of the right side: 0.670820393 Break this problem into two subproblems by setting (t + -0.5) equal to 0.670820393 and -0.670820393.Subproblem 1
t + -0.5 = 0.670820393 Simplifying t + -0.5 = 0.670820393 Reorder the terms: -0.5 + t = 0.670820393 Solving -0.5 + t = 0.670820393 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 0.670820393 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.670820393 + 0.5 t = 0.670820393 + 0.5 Combine like terms: 0.670820393 + 0.5 = 1.170820393 t = 1.170820393 Simplifying t = 1.170820393Subproblem 2
t + -0.5 = -0.670820393 Simplifying t + -0.5 = -0.670820393 Reorder the terms: -0.5 + t = -0.670820393 Solving -0.5 + t = -0.670820393 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -0.670820393 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -0.670820393 + 0.5 t = -0.670820393 + 0.5 Combine like terms: -0.670820393 + 0.5 = -0.170820393 t = -0.170820393 Simplifying t = -0.170820393Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.170820393, -0.170820393}
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